Chapter 3 (part 3) Describing Syntax and Semantics

Save this PDF as:
Size: px
Start display at page:

Download "Chapter 3 (part 3) Describing Syntax and Semantics"

Transcription

1 Chapter 3 (part 3) Describing Syntax and Semantics

2 Chapter 3 Topics Introduction The General Problem of Describing Syntax Formal Methods of Describing Syntax Attribute Grammars Describing the Meanings of Programs: Dynamic Semantics 2

3 Static semantics Context-free grammars (CFGs) cannot describe all of the syntax of programming languages Categories of constructs that are trouble: - Context-free, but cumbersome (e.g., types of operands in expressions; Java floatingpoint value cannot be assigned to integer type, but opposite legal) - Non-context-free (e.g., variables must be declared before they are used) These type of needed specification checks are referred to as Static Semantics 3

4 Attribute Grammars Attribute grammars are used to describe more of the structure of PL than we can do with CFG, e.g. to address static semantics such as type compatibility Attribute grammars (AGs) have additions to CFGs to carry some semantic info on parse tree nodes Primary value of AGs: Static semantics specification Compiler design (static semantics checking) 4

5 Attribute Grammars : Definition Def: An attribute grammar is a context-free grammar with the following additions: For each grammar symbol x there is a set A(x) of attribute values Each rule has a set of functions that define certain attributes of the nonterminals in the rule Each rule has a (possibly empty) set of predicates, which state the static semantic rules, to check for attribute consistency 5

6 Attribute Grammars: Definition Let X 0 X 1... X n be a rule Synthesized attributes - up the parse tree from children Inherited attributes - down and across parse tree Initially, there are intrinsic attributes on the leaves (such as actual types of variables, int or real) 6

7 Attribute Grammars (continued) How are attribute values computed? If all attributes were inherited, the tree could be decorated in top-down order. If all attributes were synthesized, the tree could be decorated in bottom-up order. In many cases, both kinds of attributes are used, and it is some combination of top-down and bottom-up that must be used. 7

8 Attribute Grammars: An Example Syntax <assign> -> <var> = <expr> <expr> -> <var> + <var> <var> <var> -> A B C actual_type: synthesized for <var> and <expr> expected_type: inherited for <expr> 8

9 Attribute Grammar (continued) Syntax rule: <expr> <var>[1] + <var>[2] Semantic rules: <expr>.actual_type <var>[1].actual_type Predicate: <var>[1].actual_type == <var>[2].actual_type <expr>.expected_type == <expr>.actual_type Syntax rule: <var> id Semantic rule: <var>.actual_type lookup (<var>.string) 9

10 Attribute Grammars (continued) <expr>.expected_type inherited from parent <var>[1].actual_type lookup (A) <var>[2].actual_type lookup (B) <var>[1].actual_type =? <var>[2].actual_type <expr>.actual_type <var>[1].actual_type <expr>.actual_type =? <expr>.expected_type 10

11 Attribute Grammars (continued) checking static semantic rules of a language is an essential part of all compilers. main problems of contemporary languages? 11

12 Attribute Grammars (continued) checking static semantic rules of a language is an essential part of all compilers. main problems of contemporary languages? size and complexity 12

13 Semantics There is no single widely acceptable notation or formalism for describing semantics (or dynamic semantics; meaning while executing program) Operational Semantics Describe the meaning of a program by executing its statements on a machine, either simulated or actual. The change in the state of the machine (memory, registers, etc.) defines the meaning of the statement 13

14 Operational Semantics Design an appropriate intermediate level language that describes the high level language, where the primary goal is clarity A virtual machine (interpreter) must be constructed for the intermediate language Basic idea of translating to simpler, intermediate form, often used in textbooks or manuals to explain a language 14

15 Operational Semantics Example: C for statement: for (expr1; expr2; expr 3) { } for (a=1; a<10; a++) { } Intermediate/meaning: expr1; loop: if expr2==10 goto out expr3; goto loop out: 15

16 Operational Semantics (continued) Uses of operational semantics: - Language manuals and textbooks - Teaching programming languages Evaluation - Good if used informally (language manuals, etc.) - Extremely complex if used formally (e.g., VDL=Vienna Definition Language, to describe PL/I semantics in 1972) - Operational semantics depend on programming languages of a lower level, not on mathematics 16

17 Axiomatic Semantics Based on formal logic (predicate calculus) Original purpose: formal program verification; rather than directly specifying meaning of program asks what can be proved Axioms or inference rules are defined for each statement type in the language (to allow transformations of logic expressions into more formal logic expressions) The logic expressions are called assertions Assertions are used in programming languages (eg, Java, C) 17

18 Axiomatic Semantics (continued) An assertion before a statement (a precondition) states the relationships and constraints among variables that are true at that point in execution An assertion following a statement is a postcondition A weakest precondition is the least restrictive precondition that will guarantee the postcondition 18

19 Program Proof Process The postcondition for the entire program is the desired result Work back through the program to the first statement. If the precondition on the first statement is the same as the input specification of the program, the program is correct. We ll go through some examples 19

20 Axiomatic Semantics Form Pre-, post form: {P} statement {Q} An example a = b + 1 Postcondition: {a > 1} One possible precondition: {b > 10} Weakest precondition? 20

21 Axiomatic Semantics Form Pre-, post form: {P} statement {Q} Want to find precondition that makes postcondition true An example a = b + 1 Postcondition: {a > 1} One possible precondition: {b > 10} Weakest precondition: {b > 0} 21

22 Axiomatic Semantics Form Pre-, post form: {P} statement {Q} Want to find precondition that makes postcondition true An example a = b + 1 Postcondition: {a > 1} One possible precondition: {b > 10} Weakest precondition: {b > 0} Written in pre-post form: {b>0} a = b + 1 {a>1} 22

23 Axiomatic Semantics Form More examples on board 23

24 Axiomatic Semantics: Axioms The Rule of Consequence: 24

25 Axiomatic Semantics: Axioms An inference rule for sequences of the form S1; S2 {P1} S1 {P2} {P2} S2 {P3} 25

26 Axiomatic Semantics: Axioms While loop {P} while B do S end {Q} - If we knew how many iterations through the loop we could write out as sequence and prove correctness as before for the 2 sequence example, but we don t - This is where the loop invariant (induction) comes to play 26

27 Axiomatic Semantics: Axioms Recall from CSC317 Invariant = something that does not change Loop invariant = a property about the algorithm that does not change at every iteration before the loop (it must be implied by precondition and thus hold before loop, and imply postcondition and thus hold after loop) This is usually the property we would like to prove is correct about the algorithm! 27

28 Axiomatic Semantics: Axioms Example with assert statements: Csc /workbook/findmin.html Input: Array A Output: Find minimum value in array A[1 n] Loop invariant: min is the smallest element in A[1 i-1 ] before each iteration of the loop Loop invariant asserted before loop (precondition), each time goes through loop iteration, and at end of loop (postcondition) Done through induction (initialization, maintenance, termination) 28

29 Loop Invariant I must be weak enough to be satisfied prior to the beginning of the loop, but when combined with the loop exit condition, it must be strong enough to force the truth of the postcondition Here we develop more formally how to find loop invariant using axiomatic semantics 29

30 Axiomatic Semantics: Axioms Characteristics of the loop invariant: I must meet the following conditions: Loop example: {P} while B do S end {Q} P => I -- the loop invariant must be true initially {I and B} S {I} -- I is not changed by executing the body of the loop (I and (not B)) => Q -- if I is true and B is false, Q is implied The loop terminates -- can sometimes be difficult to prove 30

31 Axiomatic Semantics: Axioms Loop invariant: formal example on the board 31

32 Evaluation of Axiomatic Semantics Developing axioms or inference rules for all of the statements in a language is difficult It is a good tool for correctness proofs, and an excellent framework for reasoning about programs Its usefulness in describing the meaning of a programming language is highly limited for language users or compiler writers 32

33 Denotational Semantics The most abstract semantics description method Originally developed by Scott and Strachey (1970) Based on recursive function theory 33

34 Denotational Semantics (continued) The process of building a denotational specification for a language: - Define a mathematical object for each language entity Define a function that maps instances of the language entities onto instances of the corresponding mathematical objects The meaning of language constructs are defined by only the values of the program's variables Called denotational because mathematical constructs denote the meaning of the corresponding entities 34

35 Denotation Semantics vs Operational Semantics Operational semantics: programming constructs translated into simpler programming language constructs Denotational semantics: programming constructs mapped into mathematical functions 35

36 Example: Binary Numbers meaning = number represents <bin_num> '0' '1' <bin_num> '0' <bin_num> 1' M bin ('0') = 0, M bin ('1') = 1 M bin (<bin_num> '0') = 2 * M bin (<bin_num>) M bin (<bin_num> '1 ) = 2 * M bin (<bin_num>)

37 Example: Binary Numbers <bin_num> <bin_num> '0' <bin_num> '1' '1' 37

38 Example: Binary Numbers 6 <bin_num> 3 <bin_num> '0' 1 <bin_num> '1' '1' Numbers on nodes represent meaning 38

39 Denotational Semantics: Program State The state of a program is the values of all its current variables s = {<i 1, v 1 >, <i 2, v 2 >,, <i n, v n >} i is name of variable and v associated value Let VARMAP be a function that, when given a variable name and a state, returns the current value of the variable VARMAP(i j, s) = v j Error we can consider is if VARMAP of a variable is undefined (special value undef) 39

40 Loop Meaning The meaning of the loop is the value of the program variables after the statements in the loop have been executed the prescribed number of times, assuming there have been no errors In essence, the loop has been converted from iteration to recursion, where the recursive control is mathematically defined by other recursive state mapping functions - Recursion, when compared to iteration, is easier to describe with mathematical rigor 40

41 Evaluation of Denotational Semantics Can be used to prove the correctness of programs Provides a rigorous way to think about programs Can be an aid to language design Has been used in compiler generation systems - feasible but complicated! Because of its complexity, it s of little use to language users 41

42 Summary BNF and context-free grammars are equivalent meta-languages Well-suited for describing the syntax of programming languages An attribute grammar is a descriptive formalism that can describe both the syntax and the semantics of a language Three primary methods of semantics description Operation, axiomatic, denotational 42

Chapter 3. Describing Syntax and Semantics ISBN

Chapter 3. Describing Syntax and Semantics ISBN Chapter 3 Describing Syntax and Semantics ISBN 0-321-49362-1 Chapter 3 Topics Introduction The General Problem of Describing Syntax Formal Methods of Describing Syntax Attribute Grammars Describing the

More information

Chapter 3. Describing Syntax and Semantics

Chapter 3. Describing Syntax and Semantics Chapter 3 Describing Syntax and Semantics Chapter 3 Topics Introduction The General Problem of Describing Syntax Formal Methods of Describing Syntax Attribute Grammars Describing the Meanings of Programs:

More information

Chapter 3. Syntax - the form or structure of the expressions, statements, and program units

Chapter 3. Syntax - the form or structure of the expressions, statements, and program units Syntax - the form or structure of the expressions, statements, and program units Semantics - the meaning of the expressions, statements, and program units Who must use language definitions? 1. Other language

More information

Chapter 3. Describing Syntax and Semantics ISBN

Chapter 3. Describing Syntax and Semantics ISBN Chapter 3 Describing Syntax and Semantics ISBN 0-321-49362-1 Chapter 3 Topics Describing the Meanings of Programs: Dynamic Semantics Copyright 2015 Pearson. All rights reserved. 2 Semantics There is no

More information

Semantics. There is no single widely acceptable notation or formalism for describing semantics Operational Semantics

Semantics. There is no single widely acceptable notation or formalism for describing semantics Operational Semantics There is no single widely acceptable notation or formalism for describing semantics Operational Describe the meaning of a program by executing its statements on a machine, either simulated or actual. The

More information

Chapter 3. Describing Syntax and Semantics

Chapter 3. Describing Syntax and Semantics Chapter 3 Describing Syntax and Semantics Chapter 3 Topics Introduction The General Problem of Describing Syntax Formal Methods of Describing Syntax Attribute Grammars Describing the Meanings of Programs:

More information

Programming Languages

Programming Languages Programming Languages Chapter 3 Describing Syntax and Semantics Instructor: Chih-Yi Chiu 邱志義 http://sites.google.com/site/programminglanguages Outline Introduction The General Problem of Describing Syntax

More information

Chapter 3: Syntax and Semantics. Syntax and Semantics. Syntax Definitions. Matt Evett Dept. Computer Science Eastern Michigan University 1999

Chapter 3: Syntax and Semantics. Syntax and Semantics. Syntax Definitions. Matt Evett Dept. Computer Science Eastern Michigan University 1999 Chapter 3: Syntax and Semantics Matt Evett Dept. Computer Science Eastern Michigan University 1999 Syntax and Semantics Syntax - the form or structure of the expressions, statements, and program units

More information

3. DESCRIBING SYNTAX AND SEMANTICS

3. DESCRIBING SYNTAX AND SEMANTICS 3. DESCRIBING SYNTAX AND SEMANTICS CSc 4330/6330 3-1 9/15 Introduction The task of providing a concise yet understandable description of a programming language is difficult but essential to the language

More information

10/30/18. Dynamic Semantics DYNAMIC SEMANTICS. Operational Semantics. An Example. Operational Semantics Definition Process

10/30/18. Dynamic Semantics DYNAMIC SEMANTICS. Operational Semantics. An Example. Operational Semantics Definition Process Dynamic Semantics DYNAMIC SEMANTICS Describe the meaning of expressions, statements, and program units No single widely acceptable notation or formalism for describing semantics Two common approaches:

More information

Syntax and Semantics

Syntax and Semantics Syntax and Semantics Syntax - The form or structure of the expressions, statements, and program units Semantics - The meaning of the expressions, statements, and program units Syntax Example: simple C

More information

Chapter 3. Describing Syntax and Semantics. Introduction. Why and How. Syntax Overview

Chapter 3. Describing Syntax and Semantics. Introduction. Why and How. Syntax Overview Chapter 3 Describing Syntax and Semantics CMSC 331, Some material 1998 by Addison Wesley Longman, Inc. 1 Introduction We usually break down the problem of defining a programming language into two parts.

More information

10/18/18. Outline. Semantic Analysis. Two types of semantic rules. Syntax vs. Semantics. Static Semantics. Static Semantics.

10/18/18. Outline. Semantic Analysis. Two types of semantic rules. Syntax vs. Semantics. Static Semantics. Static Semantics. Outline Semantic Analysis In Text: Chapter 3 Static semantics Attribute grammars Dynamic semantics Operational semantics Denotational semantics N. Meng, S. Arthur 2 Syntax vs. Semantics Syntax concerns

More information

Defining Languages GMU

Defining Languages GMU Defining Languages CS463 @ GMU How do we discuss languages? We might focus on these qualities: readability: how well does a language explicitly and clearly describe its purpose? writability: how expressive

More information

10/26/17. Attribute Evaluation Order. Attribute Grammar for CE LL(1) CFG. Attribute Grammar for Constant Expressions based on LL(1) CFG

10/26/17. Attribute Evaluation Order. Attribute Grammar for CE LL(1) CFG. Attribute Grammar for Constant Expressions based on LL(1) CFG Attribute Evaluation Order Determining attribute 2 expected_type evaluation order actual_type actual_type for any attribute grammar is a 5 complex problem, 1 [1] [2] requiring

More information

Describing Syntax and Semantics

Describing Syntax and Semantics Describing Syntax and Semantics Introduction Syntax: the form or structure of the expressions, statements, and program units Semantics: the meaning of the expressions, statements, and program units Syntax

More information

Programming Languages Third Edition

Programming Languages Third Edition Programming Languages Third Edition Chapter 12 Formal Semantics Objectives Become familiar with a sample small language for the purpose of semantic specification Understand operational semantics Understand

More information

COSC252: Programming Languages: Semantic Specification. Jeremy Bolton, PhD Adjunct Professor

COSC252: Programming Languages: Semantic Specification. Jeremy Bolton, PhD Adjunct Professor COSC252: Programming Languages: Semantic Specification Jeremy Bolton, PhD Adjunct Professor Outline I. What happens after syntactic analysis (parsing)? II. Attribute Grammars: bridging the gap III. Semantic

More information

Chapter 3. Topics. Languages. Formal Definition of Languages. BNF and Context-Free Grammars. Grammar 2/4/2019

Chapter 3. Topics. Languages. Formal Definition of Languages. BNF and Context-Free Grammars. Grammar 2/4/2019 Chapter 3. Topics The terms of Syntax, Syntax Description Method: Context-Free Grammar (Backus-Naur Form) Derivation Parse trees Ambiguity Operator precedence and associativity Extended Backus-Naur Form

More information

Chapter 3. Semantics. Topics. Introduction. Introduction. Introduction. Introduction

Chapter 3. Semantics. Topics. Introduction. Introduction. Introduction. Introduction Topics Chapter 3 Semantics Introduction Static Semantics Attribute Grammars Dynamic Semantics Operational Semantics Axiomatic Semantics Denotational Semantics 2 Introduction Introduction Language implementors

More information

Program Assignment 2 Due date: 10/20 12:30pm

Program Assignment 2 Due date: 10/20 12:30pm Decoration of parse tree for (1 + 3) * 2 N. Meng, S. Arthur 1 Program Assignment 2 Due date: 10/20 12:30pm Bitwise Manipulation of Hexidecimal Numbers CFG E E A bitwise OR E A A A ^ B bitwise XOR A B B

More information

P L. rogramming anguages. Fall COS 301 Programming Languages. Syntax & Semantics. UMaine School of Computing and Information Science

P L. rogramming anguages. Fall COS 301 Programming Languages. Syntax & Semantics. UMaine School of Computing and Information Science COS 301 P L Syntax & Semantics Syntax & semantics Syntax: Defines correctly-formed components of language Structure of expressions, statements Semantics: meaning of components Together: define the p language

More information

Syntax & Semantics. COS 301 Programming Languages

Syntax & Semantics. COS 301 Programming Languages COS 301 P L Syntax & Semantics Syntax & semantics Syntax: Defines correctly-formed components of language Structure of expressions, statements Semantics: meaning of components Together: define the p language

More information

Crafting a Compiler with C (II) Compiler V. S. Interpreter

Crafting a Compiler with C (II) Compiler V. S. Interpreter Crafting a Compiler with C (II) 資科系 林偉川 Compiler V S Interpreter Compilation - Translate high-level program to machine code Lexical Analyzer, Syntax Analyzer, Intermediate code generator(semantics Analyzer),

More information

Chapter 3. Semantics. Topics. Introduction. Introduction. Introduction. Introduction

Chapter 3. Semantics. Topics. Introduction. Introduction. Introduction. Introduction Topics Chapter 3 Semantics Introduction Static Semantics Attribute Grammars Dynamic Semantics Operational Semantics Axiomatic Semantics Denotational Semantics 2 Introduction Introduction Language implementors

More information

Static semantics. Lecture 3-6: Semantics. Attribute grammars (2) Attribute grammars. Attribute grammars example. Dynamic semantics

Static semantics. Lecture 3-6: Semantics. Attribute grammars (2) Attribute grammars. Attribute grammars example. Dynamic semantics Lecture 3-6: Semantics Static semantics Attribute grammars Dynamic semantics Denotational semantics: semantic equations Axiomatic semantics: inference rules and correctness proofs Static semantics Semantics

More information

CMSC 330: Organization of Programming Languages. Formal Semantics of a Prog. Lang. Specifying Syntax, Semantics

CMSC 330: Organization of Programming Languages. Formal Semantics of a Prog. Lang. Specifying Syntax, Semantics Recall Architecture of Compilers, Interpreters CMSC 330: Organization of Programming Languages Source Scanner Parser Static Analyzer Operational Semantics Intermediate Representation Front End Back End

More information

CMSC 330: Organization of Programming Languages. Operational Semantics

CMSC 330: Organization of Programming Languages. Operational Semantics CMSC 330: Organization of Programming Languages Operational Semantics Notes about Project 4, Parts 1 & 2 Still due today (7/2) Will not be graded until 7/11 (along with Part 3) You are strongly encouraged

More information

CSE 307: Principles of Programming Languages

CSE 307: Principles of Programming Languages CSE 307: Principles of Programming Languages Advanced Topics R. Sekar Topics 1 / 14 1. 2 / 14 Section 1 3 / 14 Semantics of Programs Syntax defines what programs are valid. Semantics defines what the valid

More information

CMSC 330: Organization of Programming Languages

CMSC 330: Organization of Programming Languages CMSC 330: Organization of Programming Languages Operational Semantics CMSC 330 Summer 2018 1 Formal Semantics of a Prog. Lang. Mathematical description of the meaning of programs written in that language

More information

Contents. Chapter 1 SPECIFYING SYNTAX 1

Contents. Chapter 1 SPECIFYING SYNTAX 1 Contents Chapter 1 SPECIFYING SYNTAX 1 1.1 GRAMMARS AND BNF 2 Context-Free Grammars 4 Context-Sensitive Grammars 8 Exercises 8 1.2 THE PROGRAMMING LANGUAGE WREN 10 Ambiguity 12 Context Constraints in Wren

More information

An Annotated Language

An Annotated Language Hoare Logic An Annotated Language State and Semantics Expressions are interpreted as functions from states to the corresponding domain of interpretation Operators have the obvious interpretation Free of

More information

In Our Last Exciting Episode

In Our Last Exciting Episode In Our Last Exciting Episode #1 Lessons From Model Checking To find bugs, we need specifications What are some good specifications? To convert a program into a model, we need predicates/invariants and

More information

Formal Semantics of Programming Languages

Formal Semantics of Programming Languages Formal Semantics of Programming Languages Mooly Sagiv Reference: Semantics with Applications Chapter 2 H. Nielson and F. Nielson http://www.daimi.au.dk/~bra8130/wiley_book/wiley.html Benefits of formal

More information

CS323 Lecture - Specifying Syntax and Semantics Last revised 1/16/09

CS323 Lecture - Specifying Syntax and Semantics Last revised 1/16/09 CS323 Lecture - Specifying Syntax and Semantics Last revised 1/16/09 Objectives: 1. To review previously-studied methods for formal specification of programming language syntax, and introduce additional

More information

Formal Semantics of Programming Languages

Formal Semantics of Programming Languages Formal Semantics of Programming Languages Mooly Sagiv Reference: Semantics with Applications Chapter 2 H. Nielson and F. Nielson http://www.daimi.au.dk/~bra8130/wiley_book/wiley.html Benefits of formal

More information

CSC 501 Semantics of Programming Languages

CSC 501 Semantics of Programming Languages CSC 501 Semantics of Programming Languages Subtitle: An Introduction to Formal Methods. Instructor: Dr. Lutz Hamel Email: hamel@cs.uri.edu Office: Tyler, Rm 251 Books There are no required books in this

More information

Chapter 4. Action Routines

Chapter 4. Action Routines Chapter 4 Action Routines Syntax and Semantics In general: Syntax form Semantics meaning In programming languages: Syntax part of the language definition that can be described via a context-free grammar

More information

Introduction to Axiomatic Semantics

Introduction to Axiomatic Semantics Introduction to Axiomatic Semantics Meeting 10, CSCI 5535, Spring 2009 Announcements Homework 3 due tonight Homework 2 is graded 13 (mean), 14 (median), out of 21 total, but Graduate class: final project

More information

FreePascal changes: user documentation

FreePascal changes: user documentation FreePascal changes: user documentation Table of Contents Jochem Berndsen February 2007 1Introduction...1 2Accepted syntax...2 Declarations...2 Statements...3 Class invariants...3 3Semantics...3 Definitions,

More information

Propositional Calculus: Boolean Functions and Expressions. CS 270: Mathematical Foundations of Computer Science Jeremy Johnson

Propositional Calculus: Boolean Functions and Expressions. CS 270: Mathematical Foundations of Computer Science Jeremy Johnson Propositional Calculus: Boolean Functions and Expressions CS 270: Mathematical Foundations of Computer Science Jeremy Johnson Propositional Calculus Objective: To provide students with the concepts and

More information

CSE 12 Abstract Syntax Trees

CSE 12 Abstract Syntax Trees CSE 12 Abstract Syntax Trees Compilers and Interpreters Parse Trees and Abstract Syntax Trees (AST's) Creating and Evaluating AST's The Table ADT and Symbol Tables 16 Using Algorithms and Data Structures

More information

1. true / false By a compiler we mean a program that translates to code that will run natively on some machine.

1. true / false By a compiler we mean a program that translates to code that will run natively on some machine. 1. true / false By a compiler we mean a program that translates to code that will run natively on some machine. 2. true / false ML can be compiled. 3. true / false FORTRAN can reasonably be considered

More information

Lecture 5 - Axiomatic semantics

Lecture 5 - Axiomatic semantics Program Verification March 2014 Lecture 5 - Axiomatic semantics Lecturer: Noam Rinetzky Scribes by: Nir Hemed 1.1 Axiomatic semantics The development of the theory is contributed to Robert Floyd, C.A.R

More information

Lectures 20, 21: Axiomatic Semantics

Lectures 20, 21: Axiomatic Semantics Lectures 20, 21: Axiomatic Semantics Polyvios Pratikakis Computer Science Department, University of Crete Type Systems and Static Analysis Based on slides by George Necula Pratikakis (CSD) Axiomatic Semantics

More information

MIDTERM EXAMINATION - CS130 - Spring 2005

MIDTERM EXAMINATION - CS130 - Spring 2005 MIDTERM EAMINATION - CS130 - Spring 2005 Your full name: Your UCSD ID number: This exam is closed book and closed notes Total number of points in this exam: 231 + 25 extra credit This exam counts for 25%

More information

COS 320. Compiling Techniques

COS 320. Compiling Techniques Topic 5: Types COS 320 Compiling Techniques Princeton University Spring 2016 Lennart Beringer 1 Types: potential benefits (I) 2 For programmers: help to eliminate common programming mistakes, particularly

More information

COMP-421 Compiler Design. Presented by Dr Ioanna Dionysiou

COMP-421 Compiler Design. Presented by Dr Ioanna Dionysiou COMP-421 Compiler Design Presented by Dr Ioanna Dionysiou Administrative! Any questions about the syllabus?! Course Material available at www.cs.unic.ac.cy/ioanna! Next time reading assignment [ALSU07]

More information

Semantic Analysis Type Checking

Semantic Analysis Type Checking Semantic Analysis Type Checking Maryam Siahbani CMPT 379 * Slides are modified version of Schwarz s compiler course at Stanford 4/8/2016 1 Type Checking Type errors arise when operations are performed

More information

Note that in this definition, n + m denotes the syntactic expression with three symbols n, +, and m, not to the number that is the sum of n and m.

Note that in this definition, n + m denotes the syntactic expression with three symbols n, +, and m, not to the number that is the sum of n and m. CS 6110 S18 Lecture 8 Structural Operational Semantics and IMP Today we introduce a very simple imperative language, IMP, along with two systems of rules for evaluation called small-step and big-step semantics.

More information

Abstract Interpretation

Abstract Interpretation Abstract Interpretation Ranjit Jhala, UC San Diego April 22, 2013 Fundamental Challenge of Program Analysis How to infer (loop) invariants? Fundamental Challenge of Program Analysis Key issue for any analysis

More information

SEQUENCES, MATHEMATICAL INDUCTION, AND RECURSION

SEQUENCES, MATHEMATICAL INDUCTION, AND RECURSION CHAPTER 5 SEQUENCES, MATHEMATICAL INDUCTION, AND RECURSION Alessandro Artale UniBZ - http://www.inf.unibz.it/ artale/ SECTION 5.5 Application: Correctness of Algorithms Copyright Cengage Learning. All

More information

axiomatic semantics involving logical rules for deriving relations between preconditions and postconditions.

axiomatic semantics involving logical rules for deriving relations between preconditions and postconditions. CS 6110 S18 Lecture 18 Denotational Semantics 1 What is Denotational Semantics? So far we have looked at operational semantics involving rules for state transitions, definitional semantics involving translations

More information

AXIOMS OF AN IMPERATIVE LANGUAGE PARTIAL CORRECTNESS WEAK AND STRONG CONDITIONS. THE AXIOM FOR nop

AXIOMS OF AN IMPERATIVE LANGUAGE PARTIAL CORRECTNESS WEAK AND STRONG CONDITIONS. THE AXIOM FOR nop AXIOMS OF AN IMPERATIVE LANGUAGE We will use the same language, with the same abstract syntax that we used for operational semantics. However, we will only be concerned with the commands, since the language

More information

Part II. Hoare Logic and Program Verification. Why specify programs? Specification and Verification. Code Verification. Why verify programs?

Part II. Hoare Logic and Program Verification. Why specify programs? Specification and Verification. Code Verification. Why verify programs? Part II. Hoare Logic and Program Verification Part II. Hoare Logic and Program Verification Dilian Gurov Props: Models: Specs: Method: Tool: safety of data manipulation source code logic assertions Hoare

More information

This is already grossly inconvenient in present formalisms. Why do we want to make this convenient? GENERAL GOALS

This is already grossly inconvenient in present formalisms. Why do we want to make this convenient? GENERAL GOALS 1 THE FORMALIZATION OF MATHEMATICS by Harvey M. Friedman Ohio State University Department of Mathematics friedman@math.ohio-state.edu www.math.ohio-state.edu/~friedman/ May 21, 1997 Can mathematics be

More information

Harvard School of Engineering and Applied Sciences CS 152: Programming Languages

Harvard School of Engineering and Applied Sciences CS 152: Programming Languages Harvard School of Engineering and Applied Sciences CS 152: Programming Languages Lecture 19 Tuesday, April 3, 2018 1 Introduction to axiomatic semantics The idea in axiomatic semantics is to give specifications

More information

A programming language requires two major definitions A simple one pass compiler

A programming language requires two major definitions A simple one pass compiler A programming language requires two major definitions A simple one pass compiler [Syntax: what the language looks like A context-free grammar written in BNF (Backus-Naur Form) usually suffices. [Semantics:

More information

Chapter 4 - Semantic Analysis. June 2, 2015

Chapter 4 - Semantic Analysis. June 2, 2015 Chapter 4 - Semantic Analysis June 2, 2015 The role of the semantic analyzer Compilers use semantic analysis to enforce the static semantic rules of a language It is hard to generalize the exact boundaries

More information

Goals: Define the syntax of a simple imperative language Define a semantics using natural deduction 1

Goals: Define the syntax of a simple imperative language Define a semantics using natural deduction 1 Natural Semantics Goals: Define the syntax of a simple imperative language Define a semantics using natural deduction 1 1 Natural deduction is an instance of first-order logic; that is, it is the formal

More information

Intro to semantics; Small-step semantics Lecture 1 Tuesday, January 29, 2013

Intro to semantics; Small-step semantics Lecture 1 Tuesday, January 29, 2013 Harvard School of Engineering and Applied Sciences CS 152: Programming Languages Lecture 1 Tuesday, January 29, 2013 1 Intro to semantics What is the meaning of a program? When we write a program, we use

More information

Type Inference Systems. Type Judgments. Deriving a Type Judgment. Deriving a Judgment. Hypothetical Type Judgments CS412/CS413

Type Inference Systems. Type Judgments. Deriving a Type Judgment. Deriving a Judgment. Hypothetical Type Judgments CS412/CS413 Type Inference Systems CS412/CS413 Introduction to Compilers Tim Teitelbaum Type inference systems define types for all legal programs in a language Type inference systems are to type-checking: As regular

More information

Outline. Introduction. 2 Proof of Correctness. 3 Final Notes. Precondition P 1 : Inputs include

Outline. Introduction. 2 Proof of Correctness. 3 Final Notes. Precondition P 1 : Inputs include Outline Computer Science 331 Correctness of Algorithms Mike Jacobson Department of Computer Science University of Calgary Lectures #2-4 1 What is a? Applications 2 Recursive Algorithms 3 Final Notes Additional

More information

Semantic Analysis. CSE 307 Principles of Programming Languages Stony Brook University

Semantic Analysis. CSE 307 Principles of Programming Languages Stony Brook University Semantic Analysis CSE 307 Principles of Programming Languages Stony Brook University http://www.cs.stonybrook.edu/~cse307 1 Role of Semantic Analysis Syntax vs. Semantics: syntax concerns the form of a

More information

The Formal Semantics of Programming Languages An Introduction. Glynn Winskel. The MIT Press Cambridge, Massachusetts London, England

The Formal Semantics of Programming Languages An Introduction. Glynn Winskel. The MIT Press Cambridge, Massachusetts London, England The Formal Semantics of Programming Languages An Introduction Glynn Winskel The MIT Press Cambridge, Massachusetts London, England Series foreword Preface xiii xv 1 Basic set theory 1 1.1 Logical notation

More information

Informal Semantics of Data. semantic specification names (identifiers) attributes binding declarations scope rules visibility

Informal Semantics of Data. semantic specification names (identifiers) attributes binding declarations scope rules visibility Informal Semantics of Data semantic specification names (identifiers) attributes binding declarations scope rules visibility 1 Ways to Specify Semantics Standards Documents (Language Definition) Language

More information

Introduction to Axiomatic Semantics (1/2)

Introduction to Axiomatic Semantics (1/2) #1 Introduction to Axiomatic Semantics (1/2) How s The Homework Going? Remember that you can t just define a meaning function in terms of itself you must use some fixed point machinery. #2 #3 Observations

More information

Semantics of programming languages

Semantics of programming languages Semantics of programming languages Informatics 2A: Lecture 28 Mary Cryan School of Informatics University of Edinburgh mcryan@inf.ed.ac.uk 21 November 2018 1 / 18 Two parallel pipelines A large proportion

More information

6. Hoare Logic and Weakest Preconditions

6. Hoare Logic and Weakest Preconditions 6. Hoare Logic and Weakest Preconditions Program Verification ETH Zurich, Spring Semester 07 Alexander J. Summers 30 Program Correctness There are many notions of correctness properties for a given program

More information

Semantic Analysis. Lecture 9. February 7, 2018

Semantic Analysis. Lecture 9. February 7, 2018 Semantic Analysis Lecture 9 February 7, 2018 Midterm 1 Compiler Stages 12 / 14 COOL Programming 10 / 12 Regular Languages 26 / 30 Context-free Languages 17 / 21 Parsing 20 / 23 Extra Credit 4 / 6 Average

More information

Programming Languages, Summary CSC419; Odelia Schwartz

Programming Languages, Summary CSC419; Odelia Schwartz Programming Languages, Summary CSC419; Odelia Schwartz Chapter 1 Topics Reasons for Studying Concepts of Programming Languages Programming Domains Language Evaluation Criteria Influences on Language Design

More information

CS2104 Prog. Lang. Concepts

CS2104 Prog. Lang. Concepts CS2104 Prog. Lang. Concepts Operational Semantics Abhik Roychoudhury Department of Computer Science National University of Singapore Organization An imperative language IMP Formalizing the syntax of IMP

More information

MIDTERM EXAM (Solutions)

MIDTERM EXAM (Solutions) MIDTERM EXAM (Solutions) Total Score: 100, Max. Score: 83, Min. Score: 26, Avg. Score: 57.3 1. (10 pts.) List all major categories of programming languages, outline their definitive characteristics and

More information

EDAN65: Compilers, Lecture 04 Grammar transformations: Eliminating ambiguities, adapting to LL parsing. Görel Hedin Revised:

EDAN65: Compilers, Lecture 04 Grammar transformations: Eliminating ambiguities, adapting to LL parsing. Görel Hedin Revised: EDAN65: Compilers, Lecture 04 Grammar transformations: Eliminating ambiguities, adapting to LL parsing Görel Hedin Revised: 2017-09-04 This lecture Regular expressions Context-free grammar Attribute grammar

More information

Com S 541. Programming Languages I

Com S 541. Programming Languages I Programming Languages I Lecturer: TA: Markus Lumpe Department of Computer Science 113 Atanasoff Hall http://www.cs.iastate.edu/~lumpe/coms541.html TR 12:40-2, W 5 Pramod Bhanu Rama Rao Office hours: TR

More information

Lecture 15 CIS 341: COMPILERS

Lecture 15 CIS 341: COMPILERS Lecture 15 CIS 341: COMPILERS Announcements HW4: OAT v. 1.0 Parsing & basic code generation Due: March 28 th No lecture on Thursday, March 22 Dr. Z will be away Zdancewic CIS 341: Compilers 2 Adding Integers

More information

7. Introduction to Denotational Semantics. Oscar Nierstrasz

7. Introduction to Denotational Semantics. Oscar Nierstrasz 7. Introduction to Denotational Semantics Oscar Nierstrasz Roadmap > Syntax and Semantics > Semantics of Expressions > Semantics of Assignment > Other Issues References > D. A. Schmidt, Denotational Semantics,

More information

Lecture 11 Lecture 11 Nov 5, 2014

Lecture 11 Lecture 11 Nov 5, 2014 Formal Verification/Methods Lecture 11 Lecture 11 Nov 5, 2014 Formal Verification Formal verification relies on Descriptions of the properties or requirements Descriptions of systems to be analyzed, and

More information

CSCI312 Principles of Programming Languages!

CSCI312 Principles of Programming Languages! CSCI312 Principles of Programming Languages! Chapter 2 Syntax! Xu Liu Review! Principles of PL syntax, naming, types, semantics Paradigms of PL design imperative, OO, functional, logic What makes a successful

More information

Semantic Analysis Attribute Grammars

Semantic Analysis Attribute Grammars Semantic Analysis Attribute Grammars Martin Sulzmann Martin Sulzmann Semantic Analysis Attribute Grammars 1 / 18 Syntax versus Semantics Syntax Analysis When is a program syntactically valid? Formalism:

More information

Definition: A context-free grammar (CFG) is a 4- tuple. variables = nonterminals, terminals, rules = productions,,

Definition: A context-free grammar (CFG) is a 4- tuple. variables = nonterminals, terminals, rules = productions,, CMPSCI 601: Recall From Last Time Lecture 5 Definition: A context-free grammar (CFG) is a 4- tuple, variables = nonterminals, terminals, rules = productions,,, are all finite. 1 ( ) $ Pumping Lemma for

More information

Hoare Logic. COMP2600 Formal Methods for Software Engineering. Rajeev Goré

Hoare Logic. COMP2600 Formal Methods for Software Engineering. Rajeev Goré Hoare Logic COMP2600 Formal Methods for Software Engineering Rajeev Goré Australian National University Semester 2, 2016 (Slides courtesy of Ranald Clouston) COMP 2600 Hoare Logic 1 Australian Capital

More information

The Rule of Constancy(Derived Frame Rule)

The Rule of Constancy(Derived Frame Rule) The Rule of Constancy(Derived Frame Rule) The following derived rule is used on the next slide The rule of constancy {P } C {Q} {P R} C {Q R} where no variable assigned to in C occurs in R Outline of derivation

More information

Program Analysis: Lecture 02 Page 1 of 32

Program Analysis: Lecture 02 Page 1 of 32 Program Analysis: Lecture 02 Page 1 of 32 Program Analysis/ Mooly Sagiv Lecture 1, 31/10/2012 Operational Semantics Notes by: Kalev Alpernas As background to the subject of Program Analysis, we will first

More information

A simple syntax-directed

A simple syntax-directed Syntax-directed is a grammaroriented compiling technique Programming languages: Syntax: what its programs look like? Semantic: what its programs mean? 1 A simple syntax-directed Lexical Syntax Character

More information

Foundations: Syntax, Semantics, and Graphs

Foundations: Syntax, Semantics, and Graphs Foundations: Syntax, Semantics, and Graphs Testing, Quality Assurance, and Maintenance Winter 2018 Prof. Arie Gurfinkel based on slides by Ruzica Pizkac, Claire Le Goues, Lin Tan, Marsha Chechik, and others

More information

Handout 9: Imperative Programs and State

Handout 9: Imperative Programs and State 06-02552 Princ. of Progr. Languages (and Extended ) The University of Birmingham Spring Semester 2016-17 School of Computer Science c Uday Reddy2016-17 Handout 9: Imperative Programs and State Imperative

More information

Relation Overriding. Syntax and Semantics. Simple Semantic Domains. Operational Semantics

Relation Overriding. Syntax and Semantics. Simple Semantic Domains. Operational Semantics SE3E03, 2006 1.59 61 Syntax and Semantics Syntax Shape of PL constructs What are the tokens of the language? Lexical syntax, word level How are programs built from tokens? Mostly use Context-Free Grammars

More information

Semantics of programming languages

Semantics of programming languages Semantics of programming languages Informatics 2A: Lecture 27 Alex Simpson School of Informatics University of Edinburgh als@inf.ed.ac.uk 18 November, 2014 1 / 18 Two parallel pipelines A large proportion

More information

Chapter 27 Formal Specification

Chapter 27 Formal Specification Chapter 27 Formal Specification Chapter 27 Formal Specification Slide 1 Objectives To explain why formal specification helps discover problems in system requirements. To describe the use of: Algebraic

More information

More Assigned Reading and Exercises on Syntax (for Exam 2)

More Assigned Reading and Exercises on Syntax (for Exam 2) More Assigned Reading and Exercises on Syntax (for Exam 2) 1. Read sections 2.3 (Lexical Syntax) and 2.4 (Context-Free Grammars) on pp. 33 41 of Sethi. 2. Read section 2.6 (Variants of Grammars) on pp.

More information

Chapter 2 & 3: Representations & Reasoning Systems (2.2)

Chapter 2 & 3: Representations & Reasoning Systems (2.2) Chapter 2 & 3: A Representation & Reasoning System & Using Definite Knowledge Representations & Reasoning Systems (RRS) (2.2) Simplifying Assumptions of the Initial RRS (2.3) Datalog (2.4) Semantics (2.5)

More information

Unit-1. Evaluation of programming languages:

Unit-1. Evaluation of programming languages: Evaluation of programming languages: 1. Zuse s Plankalkül 2. Pseudocodes 3. The IBM 704 and Fortran 4. Functional Programming: LISP 5. The First Step Toward Sophistication: ALGOL 60 6. Computerizing Business

More information

Introduction to Denotational Semantics. Class Likes/Dislikes Survey. Dueling Semantics. Denotational Semantics Learning Goals. You re On Jeopardy!

Introduction to Denotational Semantics. Class Likes/Dislikes Survey. Dueling Semantics. Denotational Semantics Learning Goals. You re On Jeopardy! Introduction to Denotational Semantics Class Likes/Dislikes Survey would change [the bijection question] to be one that still tested students' recollection of set theory but that didn't take as much time

More information

Type Systems. Today. 1. Organizational Matters. 1. Organizational Matters. Lecture 1 Oct. 20th, 2004 Sebastian Maneth. 1. Organizational Matters

Type Systems. Today. 1. Organizational Matters. 1. Organizational Matters. Lecture 1 Oct. 20th, 2004 Sebastian Maneth. 1. Organizational Matters Today Type Systems 1. Organizational Matters 2. What is this course about? 3. Where do types come from? 4. Def. of the small language Expr. Its syntax and semantics. Lecture 1 Oct. 20th, 2004 Sebastian

More information

Announcements. Written Assignment 2 due today at 5:00PM. Programming Project 2 due Friday at 11:59PM. Please contact us with questions!

Announcements. Written Assignment 2 due today at 5:00PM. Programming Project 2 due Friday at 11:59PM. Please contact us with questions! Type-Checking Announcements Written Assignment 2 due today at 5:00PM. Programming Project 2 due Friday at 11:59PM. Please contact us with questions! Stop by office hours! Email the staff list! Ask on Piazza!

More information

Introduction to Axiomatic Semantics (1/2)

Introduction to Axiomatic Semantics (1/2) #1 Introduction to Axiomatic Semantics (1/2) How s The Homework Going? Remember: just do the counterexample guided abstraction refinement part of DPLL(T). If you notice any other errors, those are good

More information

The semantics of a programming language is concerned with the meaning of programs, that is, how programs behave when executed on computers.

The semantics of a programming language is concerned with the meaning of programs, that is, how programs behave when executed on computers. Semantics The semantics of a programming language is concerned with the meaning of programs, that is, how programs behave when executed on computers. The semantics of a programming language assigns a precise

More information

Tail Calls. CMSC 330: Organization of Programming Languages. Tail Recursion. Tail Recursion (cont d) Names and Binding. Tail Recursion (cont d)

Tail Calls. CMSC 330: Organization of Programming Languages. Tail Recursion. Tail Recursion (cont d) Names and Binding. Tail Recursion (cont d) CMSC 330: Organization of Programming Languages Tail Calls A tail call is a function call that is the last thing a function does before it returns let add x y = x + y let f z = add z z (* tail call *)

More information

Topic 6: Types COS 320. Compiling Techniques. Princeton University Spring Prof. David August. Adapted from slides by Aarne Ranta

Topic 6: Types COS 320. Compiling Techniques. Princeton University Spring Prof. David August. Adapted from slides by Aarne Ranta Topic 6: Types COS 320 Compiling Techniques Princeton University Spring 2015 Prof. David August 1 Adapted from slides by Aarne Ranta Types What is a type? Type Checking: Helps find language-level errors:

More information